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Prover9---2026-6A.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : Prover9---2026-6A
% Problem  : PUZ056-2.005 : TPTP v9.3.1. Released v3.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:23:14 AM UTC 2026

% Result   : Unsatisfiable 0.12s 0.45s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   48
%            Number of leaves      :   13
% Syntax   : Number of formulae    :  110 (  48 unt;   0 def)
%            Number of atoms       :  302 (   0 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  401 ( 209   ~; 192   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-5 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :  163 (  18 sgn  30   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(rule1,axiom,
    ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
      ( p(VAR_5,VAR_1,VAR_2,VAR_3,VAR_4)
      | ~ p(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4) ),
    file('theBenchmark.p',rule1) ).

cnf(c_1,plain,
    ( p(F,B,C,D,E)
    | ~ p(A,B,C,D,E) ),
    inference(clausify,[status(thm)],[rule1]) ).

fof(rule2,axiom,
    ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
      ( p(VAR_0,VAR_5,VAR_2,VAR_3,VAR_4)
      | ~ neq(VAR_0,VAR_5)
      | ~ neq(VAR_0,VAR_1)
      | ~ p(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4) ),
    file('theBenchmark.p',rule2) ).

cnf(c_2,plain,
    ( p(A,F,C,D,E)
    | ~ neq(A,F)
    | ~ neq(A,B)
    | ~ p(A,B,C,D,E) ),
    inference(clausify,[status(thm)],[rule2]) ).

fof(rule3,axiom,
    ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
      ( p(VAR_0,VAR_1,VAR_5,VAR_3,VAR_4)
      | ~ neq(VAR_1,VAR_5)
      | ~ neq(VAR_1,VAR_2)
      | ~ neq(VAR_0,VAR_5)
      | ~ neq(VAR_0,VAR_2)
      | ~ p(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4) ),
    file('theBenchmark.p',rule3) ).

cnf(c_3,plain,
    ( p(A,B,F,D,E)
    | ~ neq(B,F)
    | ~ neq(B,C)
    | ~ neq(A,F)
    | ~ neq(A,C)
    | ~ p(A,B,C,D,E) ),
    inference(clausify,[status(thm)],[rule3]) ).

fof(rule4,axiom,
    ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
      ( p(VAR_0,VAR_1,VAR_2,VAR_5,VAR_4)
      | ~ neq(VAR_2,VAR_5)
      | ~ neq(VAR_2,VAR_3)
      | ~ neq(VAR_1,VAR_5)
      | ~ neq(VAR_1,VAR_3)
      | ~ neq(VAR_0,VAR_5)
      | ~ neq(VAR_0,VAR_3)
      | ~ p(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4) ),
    file('theBenchmark.p',rule4) ).

cnf(c_4,plain,
    ( p(A,B,C,F,E)
    | ~ neq(C,F)
    | ~ neq(C,D)
    | ~ neq(B,F)
    | ~ neq(B,D)
    | ~ neq(A,F)
    | ~ neq(A,D)
    | ~ p(A,B,C,D,E) ),
    inference(clausify,[status(thm)],[rule4]) ).

fof(rule5,axiom,
    ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
      ( p(VAR_0,VAR_1,VAR_2,VAR_3,VAR_5)
      | ~ neq(VAR_3,VAR_5)
      | ~ neq(VAR_3,VAR_4)
      | ~ neq(VAR_2,VAR_5)
      | ~ neq(VAR_2,VAR_4)
      | ~ neq(VAR_1,VAR_5)
      | ~ neq(VAR_1,VAR_4)
      | ~ neq(VAR_0,VAR_5)
      | ~ neq(VAR_0,VAR_4)
      | ~ p(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4) ),
    file('theBenchmark.p',rule5) ).

cnf(c_5,plain,
    ( p(A,B,C,D,F)
    | ~ neq(D,F)
    | ~ neq(D,E)
    | ~ neq(C,F)
    | ~ neq(C,E)
    | ~ neq(B,F)
    | ~ neq(B,E)
    | ~ neq(A,F)
    | ~ neq(A,E)
    | ~ p(A,B,C,D,E) ),
    inference(clausify,[status(thm)],[rule5]) ).

fof(neq2,axiom,
    neq(s0,s1),
    file('theBenchmark.p',neq2) ).

cnf(c_7,plain,
    neq(s0,s1),
    inference(clausify,[status(thm)],[neq2]) ).

fof(neq3,axiom,
    neq(s0,s2),
    file('theBenchmark.p',neq3) ).

cnf(c_8,plain,
    neq(s0,s2),
    inference(clausify,[status(thm)],[neq3]) ).

fof(neq4,axiom,
    neq(s1,s0),
    file('theBenchmark.p',neq4) ).

cnf(c_9,plain,
    neq(s1,s0),
    inference(clausify,[status(thm)],[neq4]) ).

fof(neq6,axiom,
    neq(s1,s2),
    file('theBenchmark.p',neq6) ).

cnf(c_11,plain,
    neq(s1,s2),
    inference(clausify,[status(thm)],[neq6]) ).

fof(neq7,axiom,
    neq(s2,s0),
    file('theBenchmark.p',neq7) ).

cnf(c_12,plain,
    neq(s2,s0),
    inference(clausify,[status(thm)],[neq7]) ).

fof(neq8,axiom,
    neq(s2,s1),
    file('theBenchmark.p',neq8) ).

cnf(c_13,plain,
    neq(s2,s1),
    inference(clausify,[status(thm)],[neq8]) ).

fof(init,axiom,
    p(s0,s0,s0,s0,s0),
    file('theBenchmark.p',init) ).

cnf(c_15,plain,
    p(s0,s0,s0,s0,s0),
    inference(clausify,[status(thm)],[init]) ).

fof(goal,axiom,
    ~ p(s2,s2,s2,s2,s2),
    file('theBenchmark.p',goal) ).

cnf(c_16,plain,
    ~ p(s2,s2,s2,s2,s2),
    inference(clausify,[status(thm)],[goal]) ).

cnf(c_17,plain,
    p(A,s0,s0,s0,s0),
    inference(resolve,[status(thm)],[c_1,c_15]) ).

cnf(c_18,plain,
    ~ p(A,s2,s2,s2,s2),
    inference(resolve,[status(thm)],[c_16,c_1]) ).

cnf(c_267,plain,
    ( p(A,B,s0,s0,s0)
    | ~ neq(A,B)
    | ~ neq(A,s0) ),
    inference(resolve,[status(thm)],[c_2,c_17]) ).

cnf(c_268,plain,
    ( p(s2,A,s0,s0,s0)
    | ~ neq(s2,A) ),
    inference(resolve,[status(thm)],[c_267,c_12]) ).

cnf(c_19,plain,
    p(s2,s1,s0,s0,s0),
    inference(resolve,[status(thm)],[c_268,c_13]) ).

cnf(c_269,plain,
    ( p(s0,D,A,B,C)
    | ~ neq(s0,D)
    | ~ p(s0,s1,A,B,C) ),
    inference(resolve,[status(thm)],[c_2,c_7]) ).

cnf(c_270,plain,
    ( p(s0,s2,A,B,C)
    | ~ p(s0,s1,A,B,C) ),
    inference(resolve,[status(thm)],[c_269,c_8]) ).

cnf(c_23,plain,
    ~ p(s0,s1,s2,s2,s2),
    inference(resolve,[status(thm)],[c_270,c_18]) ).

cnf(c_29,plain,
    ~ p(A,s1,s2,s2,s2),
    inference(resolve,[status(thm)],[c_23,c_1]) ).

cnf(c_33,plain,
    p(A,s1,s0,s0,s0),
    inference(resolve,[status(thm)],[c_1,c_19]) ).

cnf(c_271,plain,
    ( p(A,s1,B,s0,s0)
    | ~ neq(s1,B)
    | ~ neq(s1,s0)
    | ~ neq(A,B)
    | ~ neq(A,s0) ),
    inference(resolve,[status(thm)],[c_3,c_33]) ).

cnf(c_272,plain,
    ( p(s1,s1,A,s0,s0)
    | ~ neq(s1,A)
    | ~ neq(s1,s0)
    | ~ neq(s1,A) ),
    inference(resolve,[status(thm)],[c_271,c_9]) ).

cnf(c_273,plain,
    ( p(s1,s1,s2,s0,s0)
    | ~ neq(s1,s2)
    | ~ neq(s1,s0) ),
    inference(resolve,[status(thm)],[c_272,c_11]) ).

cnf(c_274,plain,
    ( p(s1,s1,s2,s0,s0)
    | ~ neq(s1,s2) ),
    inference(resolve,[status(thm)],[c_273,c_9]) ).

cnf(c_35,plain,
    p(s1,s1,s2,s0,s0),
    inference(resolve,[status(thm)],[c_274,c_11]) ).

cnf(c_275,plain,
    ( p(s1,A,D,B,C)
    | ~ neq(A,D)
    | ~ neq(A,s0)
    | ~ neq(s1,D)
    | ~ p(s1,A,s0,B,C) ),
    inference(resolve,[status(thm)],[c_3,c_9]) ).

cnf(c_276,plain,
    ( p(s1,A,s2,B,C)
    | ~ neq(A,s2)
    | ~ neq(A,s0)
    | ~ p(s1,A,s0,B,C) ),
    inference(resolve,[status(thm)],[c_275,c_11]) ).

cnf(c_277,plain,
    ( p(s1,s1,s2,A,B)
    | ~ neq(s1,s2)
    | ~ p(s1,s1,s0,A,B) ),
    inference(resolve,[status(thm)],[c_276,c_9]) ).

cnf(c_278,plain,
    ( p(s1,s1,s2,A,B)
    | ~ p(s1,s1,s0,A,B) ),
    inference(resolve,[status(thm)],[c_277,c_11]) ).

cnf(c_43,plain,
    ~ p(s1,s1,s0,s2,s2),
    inference(resolve,[status(thm)],[c_278,c_29]) ).

cnf(c_49,plain,
    ~ p(A,s1,s0,s2,s2),
    inference(resolve,[status(thm)],[c_43,c_1]) ).

cnf(c_55,plain,
    p(A,s1,s2,s0,s0),
    inference(resolve,[status(thm)],[c_1,c_35]) ).

cnf(c_279,plain,
    ( p(A,B,s2,s0,s0)
    | ~ neq(A,B)
    | ~ neq(A,s1) ),
    inference(resolve,[status(thm)],[c_2,c_55]) ).

cnf(c_280,plain,
    ( p(s0,A,s2,s0,s0)
    | ~ neq(s0,A) ),
    inference(resolve,[status(thm)],[c_279,c_7]) ).

cnf(c_58,plain,
    p(s0,s2,s2,s0,s0),
    inference(resolve,[status(thm)],[c_280,c_8]) ).

cnf(c_281,plain,
    ( p(s2,D,A,B,C)
    | ~ neq(s2,D)
    | ~ p(s2,s0,A,B,C) ),
    inference(resolve,[status(thm)],[c_2,c_12]) ).

cnf(c_282,plain,
    ( p(s2,s1,A,B,C)
    | ~ p(s2,s0,A,B,C) ),
    inference(resolve,[status(thm)],[c_281,c_13]) ).

cnf(c_70,plain,
    ~ p(s2,s0,s0,s2,s2),
    inference(resolve,[status(thm)],[c_282,c_49]) ).

cnf(c_77,plain,
    ~ p(A,s0,s0,s2,s2),
    inference(resolve,[status(thm)],[c_70,c_1]) ).

cnf(c_79,plain,
    p(A,s2,s2,s0,s0),
    inference(resolve,[status(thm)],[c_1,c_58]) ).

cnf(c_283,plain,
    ( p(s0,A,B,D,C)
    | ~ neq(B,D)
    | ~ neq(B,s1)
    | ~ neq(A,D)
    | ~ neq(A,s1)
    | ~ neq(s0,D)
    | ~ p(s0,A,B,s1,C) ),
    inference(resolve,[status(thm)],[c_4,c_7]) ).

cnf(c_284,plain,
    ( p(s0,A,B,s2,C)
    | ~ neq(B,s2)
    | ~ neq(B,s1)
    | ~ neq(A,s2)
    | ~ neq(A,s1)
    | ~ p(s0,A,B,s1,C) ),
    inference(resolve,[status(thm)],[c_283,c_8]) ).

cnf(c_285,plain,
    ( p(s0,s0,A,s2,B)
    | ~ neq(A,s2)
    | ~ neq(A,s1)
    | ~ neq(s0,s2)
    | ~ p(s0,s0,A,s1,B) ),
    inference(resolve,[status(thm)],[c_284,c_7]) ).

cnf(c_286,plain,
    ( p(s0,s0,A,s2,B)
    | ~ neq(A,s2)
    | ~ neq(A,s1)
    | ~ p(s0,s0,A,s1,B) ),
    inference(resolve,[status(thm)],[c_285,c_8]) ).

cnf(c_287,plain,
    ( p(s0,s0,s0,s2,A)
    | ~ neq(s0,s2)
    | ~ p(s0,s0,s0,s1,A) ),
    inference(resolve,[status(thm)],[c_286,c_7]) ).

cnf(c_288,plain,
    ( p(s0,s0,s0,s2,A)
    | ~ p(s0,s0,s0,s1,A) ),
    inference(resolve,[status(thm)],[c_287,c_8]) ).

cnf(c_93,plain,
    ~ p(s0,s0,s0,s1,s2),
    inference(resolve,[status(thm)],[c_288,c_77]) ).

cnf(c_289,plain,
    ( p(A,s2,s2,B,s0)
    | ~ neq(s2,B)
    | ~ neq(s2,s0)
    | ~ neq(s2,B)
    | ~ neq(s2,s0)
    | ~ neq(A,B)
    | ~ neq(A,s0) ),
    inference(resolve,[status(thm)],[c_4,c_79]) ).

cnf(c_290,plain,
    ( p(s2,s2,s2,A,s0)
    | ~ neq(s2,A)
    | ~ neq(s2,s0)
    | ~ neq(s2,A)
    | ~ neq(s2,s0)
    | ~ neq(s2,A) ),
    inference(resolve,[status(thm)],[c_289,c_12]) ).

cnf(c_291,plain,
    ( p(s2,s2,s2,s1,s0)
    | ~ neq(s2,s1)
    | ~ neq(s2,s0)
    | ~ neq(s2,s1)
    | ~ neq(s2,s0) ),
    inference(resolve,[status(thm)],[c_290,c_13]) ).

cnf(c_292,plain,
    ( p(s2,s2,s2,s1,s0)
    | ~ neq(s2,s1)
    | ~ neq(s2,s0)
    | ~ neq(s2,s1) ),
    inference(resolve,[status(thm)],[c_291,c_12]) ).

cnf(c_293,plain,
    ( p(s2,s2,s2,s1,s0)
    | ~ neq(s2,s1)
    | ~ neq(s2,s0) ),
    inference(resolve,[status(thm)],[c_292,c_13]) ).

cnf(c_294,plain,
    ( p(s2,s2,s2,s1,s0)
    | ~ neq(s2,s1) ),
    inference(resolve,[status(thm)],[c_293,c_12]) ).

cnf(c_94,plain,
    p(s2,s2,s2,s1,s0),
    inference(resolve,[status(thm)],[c_294,c_13]) ).

cnf(c_110,plain,
    ~ p(A,s0,s0,s1,s2),
    inference(resolve,[status(thm)],[c_93,c_1]) ).

cnf(c_116,plain,
    p(A,s2,s2,s1,s0),
    inference(resolve,[status(thm)],[c_1,c_94]) ).

cnf(c_295,plain,
    ( p(A,B,s2,s1,s0)
    | ~ neq(A,B)
    | ~ neq(A,s2) ),
    inference(resolve,[status(thm)],[c_2,c_116]) ).

cnf(c_296,plain,
    ( p(s1,A,s2,s1,s0)
    | ~ neq(s1,A) ),
    inference(resolve,[status(thm)],[c_295,c_11]) ).

cnf(c_118,plain,
    p(s1,s0,s2,s1,s0),
    inference(resolve,[status(thm)],[c_296,c_9]) ).

cnf(c_297,plain,
    ( p(s1,D,A,B,C)
    | ~ neq(s1,D)
    | ~ p(s1,s2,A,B,C) ),
    inference(resolve,[status(thm)],[c_2,c_11]) ).

cnf(c_298,plain,
    ( p(s1,s0,A,B,C)
    | ~ p(s1,s2,A,B,C) ),
    inference(resolve,[status(thm)],[c_297,c_9]) ).

cnf(c_130,plain,
    ~ p(s1,s2,s0,s1,s2),
    inference(resolve,[status(thm)],[c_298,c_110]) ).

cnf(c_140,plain,
    p(A,s0,s2,s1,s0),
    inference(resolve,[status(thm)],[c_1,c_118]) ).

cnf(c_151,plain,
    ~ p(A,s2,s0,s1,s2),
    inference(resolve,[status(thm)],[c_130,c_1]) ).

cnf(c_299,plain,
    ( p(A,s0,B,s1,s0)
    | ~ neq(s0,B)
    | ~ neq(s0,s2)
    | ~ neq(A,B)
    | ~ neq(A,s2) ),
    inference(resolve,[status(thm)],[c_3,c_140]) ).

cnf(c_300,plain,
    ( p(s0,s0,A,s1,s0)
    | ~ neq(s0,A)
    | ~ neq(s0,s2)
    | ~ neq(s0,A) ),
    inference(resolve,[status(thm)],[c_299,c_8]) ).

cnf(c_301,plain,
    ( p(s0,s0,s1,s1,s0)
    | ~ neq(s0,s1)
    | ~ neq(s0,s2) ),
    inference(resolve,[status(thm)],[c_300,c_7]) ).

cnf(c_302,plain,
    ( p(s0,s0,s1,s1,s0)
    | ~ neq(s0,s1) ),
    inference(resolve,[status(thm)],[c_301,c_8]) ).

cnf(c_164,plain,
    p(s0,s0,s1,s1,s0),
    inference(resolve,[status(thm)],[c_302,c_7]) ).

cnf(c_303,plain,
    ( p(s2,A,D,B,C)
    | ~ neq(A,D)
    | ~ neq(A,s1)
    | ~ neq(s2,D)
    | ~ p(s2,A,s1,B,C) ),
    inference(resolve,[status(thm)],[c_3,c_13]) ).

cnf(c_304,plain,
    ( p(s2,A,s0,B,C)
    | ~ neq(A,s0)
    | ~ neq(A,s1)
    | ~ p(s2,A,s1,B,C) ),
    inference(resolve,[status(thm)],[c_303,c_12]) ).

cnf(c_305,plain,
    ( p(s2,s2,s0,A,B)
    | ~ neq(s2,s0)
    | ~ p(s2,s2,s1,A,B) ),
    inference(resolve,[status(thm)],[c_304,c_13]) ).

cnf(c_306,plain,
    ( p(s2,s2,s0,A,B)
    | ~ p(s2,s2,s1,A,B) ),
    inference(resolve,[status(thm)],[c_305,c_12]) ).

cnf(c_172,plain,
    ~ p(s2,s2,s1,s1,s2),
    inference(resolve,[status(thm)],[c_306,c_151]) ).

cnf(c_179,plain,
    p(A,s0,s1,s1,s0),
    inference(resolve,[status(thm)],[c_1,c_164]) ).

cnf(c_189,plain,
    ~ p(A,s2,s1,s1,s2),
    inference(resolve,[status(thm)],[c_172,c_1]) ).

cnf(c_307,plain,
    ( p(A,B,s1,s1,s0)
    | ~ neq(A,B)
    | ~ neq(A,s0) ),
    inference(resolve,[status(thm)],[c_2,c_179]) ).

cnf(c_308,plain,
    ( p(s2,A,s1,s1,s0)
    | ~ neq(s2,A) ),
    inference(resolve,[status(thm)],[c_307,c_12]) ).

cnf(c_202,plain,
    p(s2,s1,s1,s1,s0),
    inference(resolve,[status(thm)],[c_308,c_13]) ).

cnf(c_309,plain,
    ( p(s0,D,A,B,C)
    | ~ neq(s0,D)
    | ~ p(s0,s1,A,B,C) ),
    inference(resolve,[status(thm)],[c_2,c_7]) ).

cnf(c_310,plain,
    ( p(s0,s2,A,B,C)
    | ~ p(s0,s1,A,B,C) ),
    inference(resolve,[status(thm)],[c_309,c_8]) ).

cnf(c_216,plain,
    ~ p(s0,s1,s1,s1,s2),
    inference(resolve,[status(thm)],[c_310,c_189]) ).

cnf(c_226,plain,
    p(A,s1,s1,s1,s0),
    inference(resolve,[status(thm)],[c_1,c_202]) ).

cnf(c_256,plain,
    ~ p(A,s1,s1,s1,s2),
    inference(resolve,[status(thm)],[c_216,c_1]) ).

cnf(c_311,plain,
    ( p(A,s1,s1,s1,B)
    | ~ neq(s1,B)
    | ~ neq(s1,s0)
    | ~ neq(s1,B)
    | ~ neq(s1,s0)
    | ~ neq(s1,B)
    | ~ neq(s1,s0)
    | ~ neq(A,B)
    | ~ neq(A,s0) ),
    inference(resolve,[status(thm)],[c_5,c_226]) ).

cnf(c_312,plain,
    ( p(s1,s1,s1,s1,A)
    | ~ neq(s1,A)
    | ~ neq(s1,s0)
    | ~ neq(s1,A)
    | ~ neq(s1,s0)
    | ~ neq(s1,A)
    | ~ neq(s1,s0)
    | ~ neq(s1,A) ),
    inference(resolve,[status(thm)],[c_311,c_9]) ).

cnf(c_313,plain,
    ( p(s1,s1,s1,s1,s2)
    | ~ neq(s1,s2)
    | ~ neq(s1,s0)
    | ~ neq(s1,s2)
    | ~ neq(s1,s0)
    | ~ neq(s1,s2)
    | ~ neq(s1,s0) ),
    inference(resolve,[status(thm)],[c_312,c_11]) ).

cnf(c_314,plain,
    ( p(s1,s1,s1,s1,s2)
    | ~ neq(s1,s2)
    | ~ neq(s1,s0)
    | ~ neq(s1,s2)
    | ~ neq(s1,s0)
    | ~ neq(s1,s2) ),
    inference(resolve,[status(thm)],[c_313,c_9]) ).

cnf(c_315,plain,
    ( p(s1,s1,s1,s1,s2)
    | ~ neq(s1,s2)
    | ~ neq(s1,s0)
    | ~ neq(s1,s2)
    | ~ neq(s1,s0) ),
    inference(resolve,[status(thm)],[c_314,c_11]) ).

cnf(c_316,plain,
    ( p(s1,s1,s1,s1,s2)
    | ~ neq(s1,s2)
    | ~ neq(s1,s0)
    | ~ neq(s1,s2) ),
    inference(resolve,[status(thm)],[c_315,c_9]) ).

cnf(c_317,plain,
    ( p(s1,s1,s1,s1,s2)
    | ~ neq(s1,s2)
    | ~ neq(s1,s0) ),
    inference(resolve,[status(thm)],[c_316,c_11]) ).

cnf(c_318,plain,
    ( p(s1,s1,s1,s1,s2)
    | ~ neq(s1,s2) ),
    inference(resolve,[status(thm)],[c_317,c_9]) ).

cnf(c_265,plain,
    p(s1,s1,s1,s1,s2),
    inference(resolve,[status(thm)],[c_318,c_11]) ).

cnf(c_266,plain,
    $false,
    inference(resolve,[status(thm)],[c_265,c_256]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : PUZ056-2.005 : TPTP v9.3.1. Released v3.5.0.
% 0.00/0.04  % Command  : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36  % Computer : n015.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.12/0.36  % WCLimit  : 300
% 0.12/0.36  % DateTime : Sat Sep 26 05:12:13 UTC 2026
% 0.12/0.36  % CPUTime  : 
% 0.12/0.37  % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37  % Process 3192811 was started by sandbox on n015,
% 0.12/0.37  % Sat Sep 26 05:12:13 2026
% 0.12/0.37  % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37  
% 0.12/0.37  % From the command line: assign(max_seconds, 300).
% 0.12/0.45  
% 0.12/0.45  % SZS status Unsatisfiable for theBenchmark
% 0.12/0.45  
% 0.12/0.45  % Proof 1 at 0.07 (+ 0.01) seconds.
% 0.12/0.45  % Length of proof is 45.
% 0.12/0.45  % Level of proof is 17.
% 0.12/0.45  % Maximum clause weight is 36.000.
% 0.12/0.45  % Given clauses 121.
% 0.12/0.45  
% 0.12/0.45  % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------